WASHINGTON — As members of Congress searched for a way forward on health care legislation, the rubble from the collapse of the latest Republican plan to repeal the Affordable Care Act continued to impede progress.

Senate Republicans, emerging from their weekly policy lunch, said they would not move ahead with a vote on the most recent repeal legislation, sponsored by Republican Sens. Bill Cassidy of Louisiana and Lindsey Graham of South Carolina. The public opposition from three Republican senators — John McCain of Arizona, Rand Paul of Kentucky and Susan Collins of Maine, had doomed that bill to defeat.

“The votes are not there,” said Sen. Pat Roberts, R-Kan., relaying what he described as a “joint” decision by the sponsors of the bill and Senate Majority Leader Mitch McConnell, R-Ky., to forgo a vote.

But with Republicans still promising to find some way to renew their effort to repeal the law, prospects for other, bipartisan, approaches remained clouded.

Congress faces at least two pressing deadlines: Federal money for the Children’s Health Insurance Program, or CHIP, a politically popular program that provides health coverage to some 9 million children, expires Saturday. Some states, which administer the program, have sufficient reserves to continue coverage for a significant time, but others will begin to run out of money within weeks, forcing them to start knocking children off coverage or freeze their programs.

And premiums for Obamacare plans for next year need to be finalized this week, with insurers not knowing whether the federal government will continue payments that help make costs affordable.

Lawmakers have worked on bipartisan solutions for both problems, but it remained unclear Tuesday if that work could be resumed.

House and Senate Republicans appeared deeply frustrated over their inability, as the majority in Congress, to fulfill their longtime campaign promise to end Obama’s signature health care law. They are being pummeled by conservatives and on talk radio, and worry voters will be punishing ahead of the midterm elections for the failure to deliver.

With President Donald Trump also leveling blame, McConnell gathered Republicans behind closed doors with Vice President Mike Pence to decide what to do next.

“I don’t think we should give up,” said Kentucky Sen. Paul. Roberts said that he hoped a repeal effort could be tried again later in this session of Congress.

“We’ve lost this battle but we’re going to win the war,” said Sen. Steve Daines, R-Mont.

In the House, which passed its own health care bill earlier this year, conservatives also refused to give up. Rep. Mark Meadows, R-N.C., said Tuesday that Republicans could try again in a matter of months, reviving special budget rules that allow for majority passage in the Senate after Congress dispatches with tax reform.

“Failure is not an option here,” Meadows, chairman of the House Freedom Caucus, said at a Tuesday roundtable with conservatives. “Midterms are coming up. If we have not produced something on this,” he said, Republican voters would punish lawmakers “at the ballot box.”

Others suggested Congress should abandon its partisan approach and resume bipartisan negotiations to stabilize the system and the other federal health programs now at risk of expiring.

Senate Finance Committee Chairman Orrin Hatch, R-Utah, and Sen. Ron Wyden, D-Ore., the panel’s senior Democrat, had been closing in on a compromise earlier this month to extend CHIP funding for another five years. But committee staff were pulled away to deal with the GOP repeal push.

Monday evening, as his committee wrapped up a marathon hearing on the Graham-Cassidy repeal proposal, Hatch expressed a desire to get back to the CHIP bill.

But it appears increasingly unlikely that Congress will be able to act before the authorization for federal funds expires Saturday.

Even more uncertain is the fate of a separate bipartisan effort to stabilize health insurance markets that have been buffeted by uncertainty over the fate of the health care law and continued threats by the Trump administration to undermine the markets the law created.

Senate Health Committee Chairman Lamar Alexander, R-Tenn., and the committee’s senior Democrat, Patty Murray, D-Wash., held four hearings earlier this month and were talking about a package of fixes that were broadly supported by state regulators, a bipartisan group of governors, insurers and others who work in health care.

But Alexander abruptly pulled out of the talks as Graham-Cassidy picked up steam, saying that a compromise wasn’t possible.

“My goal wasn’t just to get a bipartisan agreement, it was to get a bipartisan result. And I didn’t see any way to get one in the current political environment,” Alexander said Monday. “That environment hadn’t changed. Maybe it does change, but it hasn’t yet.”

Murray and other Democrats have been pleading with Alexander to restart the process, as have Republican and Democratic governors and health care officials from around the country.

“Patty Murray is ready to get back to the negotiating table, and we’re with her,” Sen. Tammy Duckworth, D-Ill., said. Murray has told other Democrats that she and Alexander were close to a deal when the talks were shut down, Duckworth added.

A bipartisan group of 10 governors, led by Ohio’s John Kasich, a Republican, and Colorado’s John Hickenlooper, a Democrat, wrote to Senate leaders last week asking them to move ahead with the bipartisan approach.